Tuesday, April 17, 2012

Concerns with holdings-based attribution

On my "to do list" is the task to write an article an article for The Journal of Performance Measurement(R), detailing some of my findings from research I'm doing regarding the impact of trading on the accuracy of the holdings-based approach to performance attribution. Recall that firms can either (a) use a "buy and hold" approach, that only uses the starting position weights, ignoring any intraperiod activity (holdings-based) or (b) begin with the starting position weights, and then adjust them for trades, income, corporate actions that occur across the period (transaction-based).

We have known that the use of holdings-based models can result in a "residual." Let's briefly speak about this term. A "residual" is a non-zero difference between the sum of the attribution effects and the associated excess return. It can occur in two ways: across periods, as the result of linking arithmetic attribution subperiod effects (geometric attribution doesn't have these residuals) or within a period, by the use of a holdings-based model.

And so, we recognize that there's a flaw in using just the starting holdings and ignoring the activity. But, as with the "across periods" approach, there is often the assumption that the error is proportionate to the results, meaning that one could smooth the residual across the effects without encountering much of an error. My research has shown that this isn't the case. In fact, there's a second, more significant problem: the misassignment of effects. That is, we can have, for example, the allocation effect reflecting a totally incorrect value (e.g., negative when it should be positive).

My research will continue for the next several months, and I hope to have something that speaks to this in much greater depth later this year. In the mean time, I will provide an update on my most recent findings at this year's Spaulding Group PMAR conferences.


  1. Stephen Campisi, CFAApril 17, 2012 at 7:22 AM

    I suggest you get ready for a dog fight, even with those who agree with you (like me.) Some of your comments relate to the firmly held, yet mistaken beliefs of most performance analysts. For example, compounding arithmetic attribution effects is simply dumb, and all the effort and mathematics involved in these absurd error-smoothing algorithms are simply a waste of good brain power. It is a recognized fact that you cannot compound partial returns, yet everyone who knows better continues this unsupportable activity. Why not simply add the attribution effects? That is actually more valid and representative as a method, since the attribution effects were based on an additive model. This would eliminate the "sign flip" of the elegantly simple method of pro-rating the residual term to the known time weighted excess return.

    I recall an article published in the Journal of Performance that pointed out the errors of transaction based attribution. I disagree with that perspective, but it shows that there is simply no methodology that represents the investment process while producing the desired "illusion of accuracy" when the cumulative attribution effects add to the time weighted excess return. Your commentary fails to address several shortcomings which are the real root of the problem.

    The first problem is one of perspective. Attribution is supposed to be an explanation of the results produced by the investment process. These results are a matter of PROPORTIONALITY rather than an accounting exercise where everything reconciles to a fraction of a basis point. This is lost on practically everyone involved with performance analysis - except the investment managers and the clients. These people (who have real "skin in the game") simply want to know: a) what worked and b) what didn't work. All this clamor and confusion around reconciling immaterial differences in results is just silly, as no one cares (except the pedants in performance.) We know what the excess return is and if we understand the proportions attributable to each attribution effect, then the analysis becomes simple and tightly controlled.

    Your issue is whether an attribution based on beginning values is valid. The best answer is "It depends." For many portfolios, the actual change in sector positioning and risk/style attributes are not material within any period. There is no evidence of the insane amount of trading that occurs in most of the hypothetical and exaggerated examples used by those writing performance articles who have an axe to grind. So, a holdings-based approach is a good representation for most portfolios. This is especially true for those of you who delight in the frequent calculation of attribution, another senseless waste of resources.

    The second and equally damaging problem that you assume away is the inconsistency between transaction based weightings and time weighted returns. These are contradictory terms. Time weighted return is ONLY valid with a static beginning value. If you combine TWR with a transaction-oriented weighting you generate a residual. So, you have simply changed the source of the residual with your approach; you haven't eliminated it. Don't take this as a criticism; a residual is inevitable, even if you use the only internally consistent attribution approach, which is a fully money weighted approach.

    If you use a money weighted approach then BOTH the weighting and the return take into account the internal money flows between sectors and securities, which are the essence of the active process we are trying to evaluate. Of course, the sum of the attribution results will differ from the time weighted excess return, as they are differently defined. This is where the attribution proportionalities are applied to the TW excess return. Now everyone is happy: we have TWR for reporting, we have sound attribution that reflects the manager's decision process, and our return analysis ties out to an analysis in changes in capital.

  2. Steve, thanks for the response; obviously, I struck a nerve or two. I think you need to address these items separately; you're invited to do so as a "guest blogger," if you want, to provide more focus. This piece only touched on linking, though I appreciate (but disagree) with your comments on linking arithmetic effects (you have yet to demonstrate why you think geometric has value).

    As to the rate of return method, I didn't address this here, but will in my article (and presentation): I use Modified Dietz, which (as you know)is a money-weighted approach (if we avoid linking), thus it qualifies. To ignore the transactions is a huge mistake and results in errors, as I have and will demonstrate.

  3. Stephen Campisi, LogicianApril 18, 2012 at 2:59 AM

    Let's focus on our areas of agreement:

    #1 - Attribution is a single period analysis by definition.

    This is a fundamental assumption that is often either unrecognized or ignored by many practitioners. The calculation itself implies this, since the sum of the weighted returns must be equal to the total return.

    #2 - Transactions matter.

    While you don't state this, transactions matter because they reflect decisions by the manager, and a "rule" of attribution is that it should represent the investment process. It's curious that you rarely justify your pronouncements with logical parameters, but rather talk about "errors" or other such procedural and calculation oriented claptrap. But I digress...

    Given these essential points of agreement, the only internally-consistent and logically sound conclusion is that a transaction-based attribution approach is the only valid approach. We agree on this, although we probably disagree that a holdings-based approach will suffice as long as transactions in the performance period were not material (admittedly a bit of circular logic on my part, perhaps...) The missing bit of logic that's needed here is this: the only valid weighting for a single period where transactions occur is the AVERAGE weighting. Of course, this weighting requires a money weighted return, which you failed to recognize in your analysis. You simply cannot apply a weighting that incorporates the effect of transactions with a time weighted returns, or you will generate a "residual" or error.

    As to my approval of a geometric approach to attribution (which seems like heresy to you) I have already stated that you cannot compound arithmetically-based partial returns. The two don't mix. You recognize this for currency analysis, so why can't you make the connection here? Once again, this is a matter of consistent definition rather than of mathematics (although the two agree.) And, once again you conveniently ignore my proven contention that a geometric approach is the only way to reconcile attribution results to changes in capital - something that clients care deeply about. To quote The Great One - "It's about reconciling to the end state."

    Last, you make an interesting, although unsubstantiated statement that attribution results are not proportionately equivalent depending on methodology. I disagree. Perhaps this is because I am speaking in terms of economic materiality, while you are likely referring to a purely mathematical difference that may require a few more decimal places to notice!

    Given the greater resource requirements for transaction-based attribution, this discussion is both important and useful. Clearly it's a source of controversy, easily seen in this controversy between two people who are actually in agreement (and who enjoy needling each other.)

  4. Being a blog post, I did not attempt to fully express all of the details regarding this topic; rather, I was providing high-level comments, which will be addressed in more detail in a forthcoming article.

    As to arithmetic's failings, folks like Jose Menchero have found ways to permit them to link; and, this works. Even your own naive method accomplishes this. And, I have demonstrated that these methods can yield the exact same results as the geometric method. Yes, it's true that the numbers do not naturally compound; so what? There are ways to correct for this. Is this not a standard practice when something doesn't work using standard tools, that alternative methods are found?

    As for "greater resource requirements for transaction-based attribution," I beg to differ, as the resources are actually less, as to make holdings work at all (and even here, with errors), daily must be used, while monthly is sufficient for transaction-based. And even if additional resources ARE needed, this is the cost for accuracy. Holdings-based can yield errors that can mislead. Surely you don't want that? As for proportionally equivalent, the holdings-based results are not; I have proven this. It is not a matter of adding a few decimal places.

    Your preference for geometric is hardly heresy; I would never think of you or our friend Carl Bacon as heretics simply because you prefer such an approach. My failure to appreciate its alleged superiority is perhaps my failing in comprehending, not your collective failing in sufficiently communincating its benefits. The ones Carl typically cites (compound, identical excess returns, proportionality) don't excite me; sorry.

    To state that I "rarely justify your pronouncements with logical parameters" is surprising, given my frequent attempt at expressing the logic behind my arguments, in both talks and writings. Again, the blog post wasn't intended to be the "end all" on this matter. In fact, my comments regarding multi-period were definitely not the intent of the piece; they were made only to clarify the alternative meaning of "residual." The mere appearance of these words obviously struck a chord with you, which necessitated your rather lengthy response. It's interesting that both your initial and subsequent responses are multiple times longer than the post! It takes a lot of words to go into the detail you wish to deliver; which is fine, but again, justifying linking methods was hardly the intent of the blog post.


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